The input vector \(\mathbf {u}\)  is divided into two sets: the set of \(K\)  information bits \(\mathcal {I}\) , and the set of \(N-K\)  frozen bits \(\mathcal {F}\)  whose values are known to the receiver. Without loss of generality, in this paper, all frozen bits are set to zero [1]}. Furthermore, the codeword \(\mathbf {x}\)  is modulated with binary phase-shift keying (BPSK) modulation that maps \(\left\lbrace 0,1\right\rbrace \)  to \(\left\lbrace +1,-1\right\rbrace \) . The modulated signal is then transmitted through an additive white Gaussian noise (AWGN) channel. The received signal is transformed into log-likelihood ratio (LLR) values \(\mathbf {y} = \lbrace y_0,y_1,\ldots ,y_{N-1}\rbrace \)  that is then processed for decoding.
